Quote:
Originally Posted by Aren Siekmeier
This seems to boil down to the difference between:
[1] Average distance between all unordered pairs of points
[2] Average length of all line segments
But what's the difference?
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The difference is in how you choose samples.
If you want the average distance between all unordered pairs of points, then you choose coordinates of pairs of points from a uniform random distribution, and compute the corresponding distance.
If you want the average length of all segments, you randomly choose a segment length, a segment orientation, and the coordinates of the center of the segment. Then you discard any chosen segments which are not inside the square. If you run a Monte Carlo sim of that, you'll get 0.3363
...and you'll get a pdf of L only, if you make a histogram of the data and adjust it to have an area of 1.